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This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel 1/(1 − θx) in place of the celebrated exponential kernel exp(θx) of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic… (More)

In this paper, we give three equivalent properties of the class of multivariate simple cubic natural exponential families (NEF’s). The first property says that the cumulant function of any basis of the family is a solution of some Monge-Ampère equation, the second is that the variance function satisfies a differential equation, and the third is… (More)

- Wlodek Bryc, Raouf Fakhfakh, Abdelhamid Hassairi
- J. Multivariate Analysis
- 2014

We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes family. We also investigate when the domain of means can be extended beyond the ”natural domain”.

- L El Matri, Y Falfoul, +5 authors A Chebil
- Journal francais d'ophtalmologie
- 2017

PURPOSE
To describe the contribution of multimodal imaging in the various stages of Stargardt disease (STGD).
PATIENTS AND METHODS
We retrospectively reviewed 46 eyes of 23 STGD patients with identified ABCA4 mutations. All patients underwent a complete ophthalmic examination, spectral-domain optical coherence tomography (SD-OCT), fundus autofluorescence… (More)

The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function of the first kind. We also study the generated natural exponential family. We determine the domain of the means and the… (More)

For a natural exponential family (NEF), one can associate in a natural way two standard families of conjugate priors, one on the natural parameter and the other on the mean parameter. These families of conjugate priors have been used to establish some remarkable properties and characterization results of the quadratic NEF’s. In the present paper, we show… (More)

- R Limaiem, A Hassairi, R Bouraoui, M Bouladi, L El Matri
- Journal francais d'ophtalmologie
- 2016

- A Hassairi, S Lajmi, R Zine
- 2008

Bobecka and Wesolowski (2002) have shown that, in the Olkin and Rubin characterization of the Wishart distribution (See Casalis and Letac (1996)), when we use the division algorithm defined by the quadratic representation and replace the property of invariance by the existence of twice differentiable densities, we still have a characterization of the… (More)

- A Hassairi, R Fadel, E Henocq, L G Chevance
- Annales d'oto-laryngologie et de chirurgie…
- 1985

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